Unit 2 - Motion and Forces
2-1 Speed, Velocity & Acceleration Definitions A scalar quantity has only magnitude. (eg 10 seconds, 45 meters) A vector quantity has both speed and direction. (eg 68km down) An instantaneous quantity is measured at a particular instant in time. (eg the car is traveling at 5m/s at specifically t=7sec) An average quantity is measured between two points. (eg the car traveled at an average speed of 4m/s for the first 7sec) Velocity Velocity is the distance traveled over time. v=s/t (velocity=change in displacement/time) Displacement is a vector quantity (50m east) therefore velocity is one as well. If an object has a constant velocity (no acceleration) then its average velocity would be the same as it's instantaneous velocity. If an object is accelerating its instantaneous velocity would be constantly changing. Acceleration Acceleration is the change in velocity over time. a=(v-u)/t (acceleration=(final velocity-initial velocity)/time) Acceleration is a vector quantity because velocity is a vector. Graphs Position-Time Graph When slope is 0: object is not moving When slope is positive: object is moving away from the origin When slope is negative: object is moving towards the origin The slope of a position-time graph is the object's velocity When the graph is curved the velocity is changing, the instantaneous velocity can be determined by finding the tangent Velocity-Time Graph When the graph is above zero then the object is moving away from the origin When the graph is below zero then the object is moving toward from the origin When the graph is flat a zero the object is not moving The area under the graph is the displacement The slope of the graph is the acceleration of the object Acceleration-Time Graph When the graph is above zero the object is increasing in velocity When the graph is below zero the object is decreasing in velocity The area under the graph is the velocity 2-2 Vectors and Relative Velocity Component Method 1) Find the horizontal and vertical components of the vectors 2) Add or subtract the vertical and horizontal components - if they are in the same direction add, if in opposite subtract 3) Sketch the sum of the vertical and horizontal components 4) Use Pythagorean Theorem to find the magnitude of the sum of the vectors 5) Use trigonometry to find the direction of the sum of the vectors 2-3 Uniform Acceleration and Free-Fall An object that is at a constant acceleration cannot be modeled by the equation v=s/t because its velocity is not constant. Thus the following five equation - SUVAT - are used. CAUTION: These equation will only work if acceleration is constant. CAUTION: Remember to work in SI units when using the following NOTE: This page will not derive any of the formulas Variables s: displacement (m) u: initial velocity (m/s) v: final velocity (m/s) a: acceleration (m/s2) t: time (s) NOTE: One must know at least 3 of the variables in order to find the other two Formulas s=0.5(v+u)t v=u+at s=ut-0.5at2 v2=u2+2as 2-4 Projectiles When dealing with projectiles the vertical and horizontal can be independently calculated (i.e. gravity does not effect horizontal motion and vice versa)(this means that a bullet fired from a gun, perfectly horizontally, and one drooped from the same height will hit the ground at the same time) If horizontal resistances are taken to be zero (i.e. no air resistance) then the formula v=s/t can be used since the object will be travelling at a constant velocity. If not then the SUVAT equations must be used As for the vertical motion, the SUVAT equations would have to be used. If air resistance is ignored on an object that is falling down, its acceleration would be 9.81ms-2 2-5 Forces and Free-Body Diagrams A free-body diagram is a way of representing all the forces acting on an obect. In this wiki there will not be instructions on how to make one Types of Forces There are two types of forces that act on objects; distant and contact Distant Forces Forces that act without contact All distant forces have fields Examples of distant forces include; gravity, electrical and magnetic Contact Forces Forces that act with contact Examples of contact forces include; normal, tensional and frictional Net Force The net force is the total force acting on an object Forces in the same direction add each other and those in opposite subtract An object has a net force of zero if all forces cancel each other out Mass vs Weight The mass of the object is the amount of matter in the object The weight of an object is the gravitational force acting on the object An object is difficult to move horizontally due to its mass An object is difficult to move vertically due to its weight Ways of Measuring Mass There are two ways to measure the mass on an object Internal Mass Inertial mass is determined by measuring how difficult it is the accelerate an object Gravitational Mass Gravitational mass is determined by measuring the force of gravity on an object Inertia Inertia is how difficult it is to move an object An object with a greater mass has greater inertia Inertia Applied The force of gravity on a heavy object is greater then the force of gravity on a lighter object The inertia on a heave object is the greater than that on light object Therefore the objects fall at the same velocity 2-6 Newton's Laws Newtons's laws consist of three rules that are often used in physics Newton's First Law An object with a constant position or velocity will remain at that position or velocity unless acted uppon by a net external force If Fnet=0 then Δv=0 Or as Mr Lebourveau likes to say it; things are lazy, they will not move or stop without something else helping them Newton's Second Law The force exerted by/on an object is dependent on the mass and acceleration of that object F=ma (Force= mass x acceleration) Newton's Third Law When an object exert a force on a second object, the second object exerts a force equal and opposite on the first object FAB = -FBA 2-7 Friction and Fluid Resistance Friction Friction is a force that opposes motion Kinetic Friction acts on an object that is sliding against another (eg sled sliding down a hill) Static Friction acts between two objects not sliding against one another (eg car tires rolling freely) Force of Friction FF=μ x FN (force of friction = coefficient of friction x normal force) The value of μ is greater for static friction the kinetic friction Fluid Resistance Fluid: a substance that flows (air or liquid) Like friction, fluid resistance acts against the motion of an object Air Resistance Air resistance becomes larger at higher speeds If you drop an object, it will accelerate to the point where the air resistance is equal to the gravitational force, thus the object will stop accelerating. This is called terminal velocity